What is one way states rights became a part of the slavery debate

If states have rights to establish their own laws and policies, then, in the eyes of slave-holding states, the non-slavery states would not have the right to tell the slave-holding states how to run their affairs.

After victory in war with Mexico (in 1848) and new territories were going to be added to the USA in the western regions, the debate over states rights got heated further.  The question arose as to whether the new territories/states would permit slavery or not.